Kontruksi Geometri_(Masalah 3.1, Masalah 3.2, & Masalah 3.3)_Selvia Widi Astuti_A1C020004

Summary

This tutorial walks through the use of GeoGebra to construct geometric shapes and prove key theorems. The video demonstrates how to construct angles (such as 90° and 30°), duplicate them, and form geometric figures like triangles and trapezoids. It highlights the verification of properties such as angle congruence and area relationships, using tools like angle measurement, intersection, and area calculation. The script also explains how to prove the formula for the area of a trapezoid through step-by-step construction and calculations, ensuring the validity of geometric concepts and theorems.

Takeaways

• 😀 The lesson begins by demonstrating the construction of a right angle (90°) and a 30° angle using GeoGebra.
• 😀 The constructed angles are duplicated using geometric operations, like intersecting circles and lines, to form a triangle.
• 😀 After duplicating the angles, the accuracy of the constructed angles is verified using the 'Angle' tool in GeoGebra.
• 😀 The student demonstrates that the angle formed between the two constructed angles is 60°, the result of subtracting 90° and 30°.
• 😀 The properties of triangle AMD are analyzed, and the internal angles are validated through geometric constructions and calculations.
• 😀 The lesson then moves to proving the area formula for a trapezoid, showing that it equals 1/2 * height * (base1 + base2).
• 😀 A trapezoid ABCD is constructed in GeoGebra, and the bases and height are measured using the tool.
• 😀 The area of the trapezoid is calculated using GeoGebra’s area tool, confirming the formula's validity with a result of 16.5.
• 😀 The teacher demonstrates how to calculate the components of the area formula (bases and height), and then applies the formula to verify the result.
• 😀 The area formula is confirmed by comparing the calculated result using GeoGebra with the formula, yielding the same result of 16.5.

Q & A

What is the purpose of constructing angles in the script?

The purpose of constructing angles in the script is to demonstrate the creation of specific geometric figures, like a triangle, and to show how angles can be duplicated using various tools in Geogebra. The script focuses on constructing a 90° angle and a 30° angle for further geometric operations.

How is the 90° angle constructed in the video?

The 90° angle is constructed by using the 'Angle with given size' feature in Geogebra. After selecting two points, the angle is adjusted to 90°, and a segment is drawn to complete the angle.

What is the purpose of duplicating the 90° angle in the script?

Duplicating the 90° angle is part of the process to create additional angles and geometric constructions, which ultimately help in the creation of a triangle and verifying angle properties, such as proving that two angles sum to 180° or creating a parallel line.

What role does the circle play in the angle construction?

The circle is used to help duplicate angles. By creating a circle around a specific point and using intersections, the geometric figure's symmetry and angle properties are maintained, aiding in duplicating angles like the 90° and 30° angles.

How is the angle of 30° constructed in the script?

The 30° angle is constructed using the 'Angle with given size' feature in Geogebra, selecting two points to form an angle and adjusting it to 30°. A segment is then drawn to connect the points, completing the angle.

What is the significance of creating parallel lines in the construction?

The parallel lines are crucial for proving geometric properties, such as showing that certain angles are congruent. In this case, parallel lines are used to help form and prove relationships in the constructed triangle.

How is the triangle formed in the video?

The triangle is formed by constructing a series of angles, including 90° and 30°, and using the intersection of lines and circles to create the necessary geometric relationships. The final result is a triangle with specific angle measures.

What method is used to prove that the triangle has a 60° angle?

To prove that the triangle has a 60° angle, the angle between two specific points is measured using the 'Angle' feature in Geogebra. The calculation confirms that the angle formed is indeed 60°.

How is the area of the trapezium calculated in the script?

The area of the trapezium is calculated using the 'Area' feature in Geogebra. By selecting the trapezium, the software computes the area, which is found to be 16.5 square units.

What formula is used to calculate the area of the trapezium, and how is it validated?

The formula used to calculate the area of the trapezium is (1/2) * height * (base1 + base2). The result is validated by comparing it with the area calculated by Geogebra, confirming that the two methods yield the same result of 16.5.